Base field 4.4.15529.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 6 x^2 - x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[5, 5, w - 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^8 - 12 x^6 + 38 x^4 - 35 x^2 + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w - 1]$ | $-1$ |
| 8 | $[8, 2, -w^3 + w^2 + 6 w + 1]$ | $\phantom{-}\frac{1}{2} e^7 - 6 e^5 + 18 e^3 - \frac{23}{2} e$ |
| 9 | $[9, 3, -w^3 + w^2 + 5 w + 1]$ | $-\frac{1}{2} e^7 + 6 e^5 - 19 e^3 + \frac{35}{2} e$ |
| 9 | $[9, 3, -w^3 + 2 w^2 + 3 w - 1]$ | $-e^7 + 11 e^5 - 28 e^3 + 16 e$ |
| 19 | $[19, 19, -w^3 + 2 w^2 + 4 w - 1]$ | $\phantom{-}e^5 - 10 e^3 + 17 e$ |
| 23 | $[23, 23, w^2 - 2 w - 1]$ | $-\frac{1}{2} e^7 + 6 e^5 - 19 e^3 + \frac{39}{2} e$ |
| 29 | $[29, 29, w^2 - 3 w - 1]$ | $-e^7 + 12 e^5 - 38 e^3 + 33 e$ |
| 29 | $[29, 29, -w^2 + w + 3]$ | $\phantom{-}e^6 - 11 e^4 + 27 e^2 - 11$ |
| 37 | $[37, 37, w^3 - w^2 - 5 w + 1]$ | $\phantom{-}e^7 - 12 e^5 + 38 e^3 - 33 e$ |
| 43 | $[43, 43, -w^3 + 2 w^2 + 3 w - 3]$ | $-e^6 + 10 e^4 - 18 e^2 - 3$ |
| 47 | $[47, 47, -w^2 + 2 w + 5]$ | $-e^4 + 9 e^2 - 8$ |
| 47 | $[47, 47, 2 w^3 - 2 w^2 - 11 w - 5]$ | $\phantom{-}4 e$ |
| 53 | $[53, 53, -w^3 + 2 w^2 + 2 w + 1]$ | $\phantom{-}e^4 - 7 e^2 + 8$ |
| 59 | $[59, 59, -w - 3]$ | $\phantom{-}e^4 - 7 e^2 + 6$ |
| 73 | $[73, 73, w^2 - w + 1]$ | $\phantom{-}2 e^6 - 20 e^4 + 40 e^2 - 12$ |
| 73 | $[73, 73, 2 w^3 - 2 w^2 - 12 w - 5]$ | $\phantom{-}\frac{3}{2} e^7 - 18 e^5 + 57 e^3 - \frac{97}{2} e$ |
| 79 | $[79, 79, 4 w^3 - 4 w^2 - 22 w - 7]$ | $\phantom{-}e^7 - 10 e^5 + 18 e^3 - e$ |
| 97 | $[97, 97, 2 w^3 - 3 w^2 - 9 w + 1]$ | $-2 e^7 + 23 e^5 - 64 e^3 + 37 e$ |
| 101 | $[101, 101, 2 w^2 - 2 w - 9]$ | $\phantom{-}e^6 - 10 e^4 + 16 e^2 + 7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w - 1]$ | $1$ |